Research PaperNo Access

$C_{4} C_{8} (S)$ tori which are Cayley graphs

Chunqi Liu

Nanjing Polytechnic Institute, Nanjing, Jiangsu, China

https://doi.org/10.1142/S1793830920500731Cited by:0 (Source: Crossref)

Abstract

A $C_{4} C_{8}$ net is a trivalent decoration made by alternating square $C_{4}$ and octagons $C_{8}$ . It can cover either a cylinder or a tori. Cayley graph $Cay (G, S)$ on a group $G$ with connection set $S$ has the elements of $G$ as its vertices and an edge joining $g$ and $s g$ for all $g \in S$ and $s \in S$ . Motivated by Afshari’s work, we show that the $C_{4} C_{8} (S) [n, n]$ tori are Cayley graphs by constructing a regular subgroup of the automorphism group of $C_{4} C_{8} (S) [n, n]$ .

Keywords:

AMSC: 05C25

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